How to unwrap a ring to straight gird?
To get a perfectly straight strip, select 2 points on one side of a section of your unwrapped ring (preferably one that already has 2 &quot;flat&quot; edges - such as the one at the top). Set your transform pivot point to &quot;Active element&quot;.

Scale the 2 points to 0 on whatever axis you are using (I used X) to make the points straight in line on this axis. Do this on both sides until you have a rectangle.

Now select the whole thing, keeping the &quot;rectangle&quot; selected. Press U for unwrap in the 3D viewport and select &quot;follow active quads&quot;. This will make your selection into a strip.